Added iterative runaway script

iterative_runaway_ice_albedo_feedback.py

@@ -0,0 +1,80 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+### Properties ###
+steps = 100
+
+# Data
+T_data = np.array([265, 255, 245, 235, 225, 215])
+il_data = np.array([75, 60, 45, 30, 15, 0])
+albedo_data = np.array([0.15, 0.25, 0.35, 0.45, 0.55, 0.65])
+
+# Ice latitude
+m1, b1 = np.polyfit(T_data, il_data, 1)
+
+def calc_ice_latitude(T):
+    return m1 * T + b1
+
+# Planetary albedo
+m2, b2 = np.polyfit(T_data, albedo_data, 1)
+
+def calc_albedo(T):
+    return np.clip(m2 * T + b2, 0, 1)
+
+### Constants and Data ###
+epsilon = 1
+sigma = 5.67E-8                         # W/m2 K4
+
+### Energy balance equation ###
+def calc_temperature(albedo, L):
+    return pow((L * (1 - albedo)) / (4 * epsilon * sigma), 1/4)
+
+### Iteration step ###
+def iterate(L, initial_albedo, steps):
+    T = calc_temperature(initial_albedo, L)
+    for i in range(steps):
+        albedo = calc_albedo(T)
+        new_T = calc_temperature(albedo, L)
+        T = new_T
+    return T, albedo
+
+### Loop ###
+l_range_bounds = [ 1200, 1600 ]
+
+
+current_albedo = 0.15
+temp_down = []
+l_range_down = []
+L = l_range_bounds[1]
+while L > l_range_bounds[0]-1:
+    T, current_albedo = iterate(L, current_albedo, steps)
+    temp_down.append(T)
+    L = L - 10
+    l_range_down.append(L)
+
+current_albedo = 0.65
+temp_up = []
+l_range_up = []
+L = l_range_bounds[0]
+while L < l_range_bounds[1]+1:
+    T, current_albedo = iterate(L, current_albedo, steps)
+    temp_up.append(T)
+    L = L + 10
+    l_range_up.append(L)
+
+
+### Input ###
+# L, albedo, nIters = input("").split()
+# L, albedo, nIters = [ float(L), float(albedo), int(nIters) ]
+
+# T, albedo = iterate(L, albedo, nIters)
+# print(T, " ", albedo)
+
+### Plot hysteresis ###
+plt.plot(l_range_down, temp_down, label="Cooling")
+plt.plot(l_range_up, temp_up, label="Warming")
+plt.xlabel("Solar Constant (L)")
+plt.ylabel("Equilibrium Temperature (K)")
+plt.legend()
+plt.show()